In this lesson, students continue to develop methods for computing products of decimals, including using area diagrams. They multiply decimals by expressing them as fractions, or by interpreting each decimal as a product of a whole number and a power of 10 and \(\frac1{10}\). To multiply \((0.25)⋅(1.6)\), for example, students may first multiply 0.25 by 100 and 1.6 by 10 to have whole numbers 25 and 16, multiply the whole numbers to get 400, and then multiply 400 by \(\frac1{1000}\) to invert the initial multiplication by 1,000. They may also think of 0.25 and 1.6 as \(\frac{25}{100}\) and \(\frac{16}{10}\), multiply the fractions, and then express the fractional product as a decimal.
In earlier grades, students used the area of rectangles to represent and find products of whole numbers and fractions. Here they do the same to represent and find products of decimals. They see that a rectangle that represents \(4⋅2\), for instance, can also be used to reason about \((0.4)⋅(0.2), (0.004)⋅(0.002)\), or \(40⋅20\) because they all share a common structure. In this lesson, students extend their understanding of multiplication of fractions and multiplication using area diagrams by using previous methods to multiply any pair of decimals.
Lesson overview
- 6.1 Warm-up: Which One Doesn’t Belong: Products (5 minutes)
- 6.2 Activity: Using Properties of Numbers to Reason about Multiplication (20 minutes)
- 6.3 Optional Activity: Using Area Diagrams to Reason about Multiplication (15 minutes)
- Lesson Synthesis
- 6.4 Cool-down: Finding Products of Decimals (5 minutes)
Learning goals:
- Interpret different methods for computing the product of decimals, and evaluate (orally) their usefulness.
- Justify (orally, in writing, and through other representations) where to place the decimal point in the product of two decimals with multiple non-zero digits.
Learning goals (student facing):
- Let’s look at some ways we can represent multiplication of decimals.
Learning targets (student facing):
- I know and can explain more than one way to multiply decimals using fractions and place value.
- I can use area diagrams to represent and reason about multiplication of decimals.
Glossary:
- Access the complete Grade 6 glossary.
Standards
- This lesson builds on the standard:CCSS.5.NBT.B.7MS.5.NBT.7MO.5.NBT.A.6MO.5.NBT.A.7MO.5.NBT.A.8
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/math-curriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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